Cidex 424 bis Telephone (+33) 493 775 275
F-06330 Roquefort les Pins Telefax (+33) 493 771 979
France e-mail [email protected]
BEAST
A Computer Program for Limit Equilibrium Analysis by
the Method of Slices
Report 8302 - 2
Revision 0, 5 October 1988
Revision 1, 24 April 1990
Revision 2, 15 October 1993
Revision 3, 10 August 2000
Revision 4, 24 April 2003
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CONTENTS Page
1.0 Summary... 3 2.0 General Description...
2.1 Program Identification...
2.2 Program Capabilities and Limitations...
2.3 Computer Requirements...
4 4 4 7 3.0 Engineering Documentation...
3.1 Co-ordinate System and Units...
3.2 Geometry Modelling and Shear Surfaces...
3.3 Soil Properties...
3.4 Pore Water Pressures and Forces...
3.5 Load Calculation...
3.6 Governing Equations...
3.7 Solution Procedures, Stability and Bearing Capacity...
3.8 Solution Procedures, Earth Pressures...
3.9 Solution Quality Control...
8 8 8 10 14 17 19 23 27 28 4.0 User’s Guide...
4.1 General System Description...
4.2 Input Data File NF14...
4.3 Interaction Between Program and User...
4.4 Printed Results File NF16...
4.5 Printed Results File NF17...
4.6 Warnings and Error Messages...
30 30 31 45 53 57 60 5.0 Program Maintenance...
5.1 Subroutine Description and Control Flow...
5.2 Input/Output Files...
5.3 Program Modifications, Common Area...
65 65 68 69 6.0 References... 76
Appendix A : Program Beast General Description Appendix B : Undrained Effective Stress Analysis Appendix C : Example Cases Analysed by Beast Appendix D : Soil Nails Procedures
Appendix E : Solution Procedures
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1.0 SUMMARY
The report presents the documentation of computer program BEAST. This program may be used for limit equilibrium analysis of cases involving slope stability, bearing capacity or earth pressure calcula- tions.
BEAST is an interactive menu driven program that allows the user to try different shear surfaces, to modify control parameters, etc. during the program operations.
This documentation report covers the following main topics : General Description
Gives a summary of required input values and procedures used by BEAST to solve a given problem.
Size limitations and computer requirements are presented.
Engineering Documentation
Gives a detailed description of geometry modelling, soil parameters and load calculation. The governing equations are formed and the different solution procedures that may be used by BEAST are briefly explained. More detailed descriptions are included in Appendix E.
User's Guide
Gives a detailed description of the input data file to be prepared before a case is analysed. The interactive communication between user and program is explained. The section also contains a de- scription of output generated by BEAST, including warnings and error messages.
Program Maintenance
Gives a description of subroutines, input/output files and the common area. Procedures for program modification are explained.
Examples
Appendix C to this report contains 13 examples with descriptions, input files and computed results.
These examples are intended both for self studies and for program checking purposes.
Acknowledgements
During the work with BEAST a number of colleagues have contributed with material and points of view. This includes K.H. Andersen, R.A. Lauritzsen and T. Valstad of NGI, prof. L. Grande of NTH, G. Vefling and G. Jessen of COWIconsult, S. Holmberg of R&H and prof. J.M. Duncan of the University of Virginia.
The program development was made possible by the support from COWIconsult A/S, the Norwegian
Geotechnical Institute and the AutoGRAF group. The author gratefully acknowledges their generous
contribution.
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2.0 GENERAL DESCRIPTION
2.1 Program Identification
Program Name BEAST
Program Author Carl J. Frimann Clausen Telephone (+33) (0)4 9377 5275
Cidex 424 Bis Telefax (+33) (0)4 9377 1979
F-06330 Roquefort-les-Pins E-mail [email protected] Revision 0 5 October 1988 Revision 3 10 August 2000
Revision 1 24 April 1990 Revision 4 24 April 2003 Revision 2 15 October 1993
ABSTRACT
The program can be used to analyse slope stability, bearing capacity and earth pressure problems by a general procedure of slices. Total or effective stresses may be used. Shear surfaces may be planes, circles, combined surfaces or general surfaces specified point by point.
Different solution methods may be used. Some of these methods give force and moment equilibrium for each slice, with an automatic control of the quality of the solution obtained. The geometry con- sidered is plane strain with inclusion of end surface shear stresses if wanted.
Program output includes computed safety factor or earth pressure, an indicator of the quality of the solution found, and detailed results of forces or stresses etc. for each individual slice. Plots of input data and computed results may be generated by BEAST or by a post processor program.
BEAST is written in FORTRAN-77. It is an interactive program and consists of approximately 12,000 program lines.
2.2 Program Capabilities and Limitations Soil Properties
Each point within the soil volume is assigned a soil material identification number. For each soil material the unit weight is given, and in the case of total stress analysis :
* Undrained shear strength that may vary with the inclination of the shear surface.
In the case of effective stress analysis, the following values are required : * Cohesion
* Angle of internal friction that may depend upon effective normal stress against the shear surface.
* Pore water pressure parameters (Ru,B,Ko,B2,D).
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A general variation of undrained shear strengths and pore water pressures may be specified. An undrained effective stress analysis may be carried out, i.e. the pore water pressures are calculated during the iterative solution process.
A combination of effective and total stress analysis may be carried out, where the shear strength calculated using effective strength parameters is replaced by the given undrained shear strength, if the latter is the lower of the two.
Geometry
BEAST can handle two dimensional (plane strain) cases. Shear stresses at the end surfaces can be included if wanted. The soil surface is given as a broken line point by point. A rock surface may be specified at some depth below the soil surface. In case a shear surface intersects the rock surface, the shear surface is modified to follow the rock-soil interface. Zones of rigid material, e.g. a
foundation block, may be specified. Shear surfaces that intersect such a zone are given a high safety factor.
A simple finite element type mesh is generated by BEAST to cover the soil body. This mesh may be used as a frame of reference for material properties, undrained strengths and pore water pressures.
Alternative ways for quick and simple input of such values are available as well.
Shear Surfaces
The user may choose between the following alternative methods to generate the shear surface to be analysed :
* General surfaces specified point by point and read as a part of the input file.
These surfaces may be shifted and/or stretched in the X- and Z-directions.
* Circles, either specified one by one, or generated by the program in an automatic search for the circle giving the lowest safety factor.
* Different types of combined surfaces consisting of straight lines - circles - straight lines, also with an automatic search facility.
* Straight lines (planes) in the case of active or passive earth pressure calculations.
Pore Water Pressures (PWP)
PWP values can be given by a number of different options, and combined to produce the wanted variation within the soil volume. Permanent matrix suction in fine-grained soils may be specified. Uplift and seepage forces, and the corresponding moments, are automatically computed once the PWP values have been found.
BEAST allows an undrained effective stress analysis (UESA) to be carried out. The PWP values are then calculated from effective stress changes and PWP parameters for each material type by an iterative solution process.
Given Loading
The system of slices may be subjected to the following types of loading :
* Self weight (vertical acceleration)
* Horizontal acceleration
* External free surface water pressures
* Internal water pressures (seepage forces)
* Given point forces (line loads)
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* Given soil surface normal and shear stresses
* Loads imposed by piles and/or soil nails
Solution Procedure
BEAST is based upon limit equilibrium considerations, i.e. it is assumed that the design soil strength is fully mobilised along the entire shear surface. The program finds a solution that gives both force and moment equilibrium for each slice.
A solution of this type will always require that some assumptions are being made related to unknown values, for example the interslice roughness value or the position of the normal forces against the slice faces.
The present BEAST version (revision 4, April 2003) allows different solution methods to be used.
These methods include force equilibrium with given interslice roughness, Bishop simplified, Bishop modified and a Morgenstern & Price type solution referred to as BEAST-2003.
When a solution has been obtained, BEAST will check the quality of this solution in terms of location of normal forces, interslice shear mobilisation etc. The results of this check is expressed as a
"score". This allows BEAST to modify the assumptions made, repeat the analysis, and to find the solution with the best "score" value.
Instructions and Help to the User
Considerable efforts have been put into making BEAST a user friendly program. In order to reduce the need to consult the program documentation report, the INSTRUCTION and HELP facilities may be called upon during the interactive program operation.
This allows the user to display various types of information like explanation of error and warning messages, description of input file values etc., during the interactive program operation.
Program Output
BEAST generates summary type results that are displayed at the user's screen. Detailed print of selected shear surfaces, either the best one so far, or the last one analysed, may at any time be saved on a separate print file.
This print file may also include plots of input data (Su0 or PWP at mesh nodal points) and plots of computed values along the shear surface. Detailed results from a shear surface may be saved on another print file for later use by a post processing program.
Size Limitations
The present program version (April 2003) has the following limitations on the problem sizes that can be handled :
3500 elements and 3636 nodes in the FE type mesh used to assign properties.
101 vertical sections used to give the soil surface and the bedrock surface location.
50 different soil material types.
35 horizontal layers.
150 triangles used to assign soil properties.
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25 vertical sections with given Su0 values with depth.
25 vertical sections with given PWP values with depth.
25 Su0 or PWP values at each vertical section.
50 given point forces.
20 strips with given distributed stresses.
30 general shear surfaces.
100 points on each general shear surface.
99 number of slices that each shear surface may be divided into.
75 piles and/or soil nails
The above values are set at the start of BEAST, and compared to the input values given. In case a limitation is exceeded, BEAST prints an error message and terminates the run. Procedures to be used in case these size limitations shall be changed, are given in Section 5.3.
2.3 Computer Requirements
BEAST is written in FORTRAN-77 and contains approximately 12,000 statements including comments. It needs 5 input/output files and a user's interactive terminal from which the program is operated. Terminal input/output is alphanumerical only, no graphic display unit is required.
Revision 3, 10 August 2000
The solution was extended to include piles and/or soil-nails. See Appendix D for a description of the procedures used. Soil matrix suction for different materials was introduced.
Revision 4, 24 April 2003
A number of new solution methods were included, i.e. force equilibrium, Bishop simplified, Bishop modified and BEAST-2003. The procedures used for the Swedish combined analysis have been completely re-written. The shear surface exit angle through frictional materials may automatically be reduced if needed. Materials with negative strength are used to flag the presence of rigid zones, e.g.
a foundation base.
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3.0 ENGINEERING DOCUMENTATION
3.1 Co-ordinate System and Units
BEAST uses an orthogonal co-ordinate system with a horizontal X-axis, positive either to the right or to the left, and with a vertical Z-axis that must be positive downwards.
Figure 3.1.1 : Acceptable Co-ordinate Systems
The above figure gives examples of the two co-ordinate systems that may be used. Note that in both cases the horizontal displacement of the system of slices will be in the positive X direction.
At several places in this document reference is made to "right" and "left". Whenever these terms are used, it is assumed that the co-ordinate system is one with the positive X going from the left to the right.
BEAST will accept any system of units, it is the responsibility of the user to ensure that a consistent system is used. In order to allow program output in any system of units, independent of the input data units used, BEAST reads a length and a force multiplier at the start of the input data. All values are multiplied by these values immediately after they have been read from the formatted input file NF15.
Note that values read from the user's keyboard during the interactive program operation are not multiplied by these unit conversion factors.
3.2 Geometry Modelling and Shear Surfaces
The geometry of the plane strain system to be analysed is described by means of a number of
vertical X-lines. At each of these lines the position of the soil surface and the rock surface is
specified, together with instructions to BEAST on how detailed the finite element type mesh to be
generated shall be. See Section 4.2 for detailed instructions and an example. Mesh nodal points and
elements numbering system used is shown on Figure 3.3.2.
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Each element in the generated mesh is given a material identification number. However, in order to allow easy specification of horizontal layering, and also to allow a completely general variation of material properties, the user may specify a number of horizontal layers and/or a number of triangles for which the material identification number is given.
Once the co-ordinates of any point (X,Z) is given, BEAST can thus find the material identification number at that point, and the corresponding soil properties. The detailed procedure used is explained at the start of Section 3.3.
With the main geometry known, BEAST needs a shear surface for which either stability/bearing capacity or earth pressure calculations shall be carried out. BEAST can handle the following types of shear surfaces :
* A straight line, for earth pressure calculations only.
* Circles.
* Combined surfaces consisting of straight line(s) and circle(s), Figure 4.3.1.
* General shear surfaces given as a broken line between specified points.
The three first types of surfaces are generated by BEAST from data given via the user's keyboard.
General shear surfaces are read from the input data file NF15.
With the co-ordinates of points along the shear surface known, BEAST finds the two first intersections between the shear surface and the soil surface. If a geometry problem is identified, an error message is printed and the run terminated.
The body of soil enclosed by the shear surface and the soil surface may now be divided into the number of slices specified by the user. Under normal conditions equal width of all slices is used.
However, in the case of general shear surfaces, the user may specify that a slice division correspon- ding to the given points on the general shear surface shall be used.
BEAST will automatically generate extra slices when the shear surface intersects horizontal layer interfaces. This is done to avoid having two different materials at the slice bottom.
The geometry of the system to be analysed has now been established. Next step will be to assign soil property values to the different points in the system, and to compute all values that are independent of the factor of safety.
Figure 3.2.1 below shows a typical slice with the corner point numbering and face numbering system
that is used by BEAST. The centre point 5 is found as the centre of gravity of the slice.
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Figure 3.2.1 : Slice Corner Point and Face Numbering System.
3.3 Soil Properties
A given point (X,Z) is assigned a material identification number by the following steps : 1. Find the mesh element number that the point falls inside, and give
the point the material number assigned to that element.
2. If horizontal layers were specified, replace the above by the material number corresponding to the layer inside which the point falls.
3. If material triangles were specified, and the point falls inside or on the side line of such a triangle, replace the above by the material number corresponding to the first triangle inside which the point falls.
For each material a complete set of soil parameters, to be used for both total and effective stress analysis, has been given as part of the input data read from file NF15. These soil property values are described in detail below.
Total Unit Weight
The unit weights given are assumed to be total values, i.e. they include weight of both soil particles and water. For a system completely submerged in water the effective unit weights may be used, provided the hydrostatic pore water pressure (PWP) is set to zero. See next section for more details.
Undrained Shear Strengths
BEAST allows the user to specify any variation of undrained shear strength (Su) values in the horizontal and the vertical direction. These Su values may either be isotropic, i.e. independent of the inclination of the shear surface, or anisotropic values corresponding to +45,0,-45 degrees shear surface inclination may be specified, see Figure 3.3.1.
5 X
Z 1
2
3 4
Face 2
Face 3
Face 1
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For each material the three ratios SuA/Su0, SuD/Su0 and SuP/Su0 are given. With known Su0 (see below) and material id. the anisotropic Su values corresponding to active triaxial, direct simple shear and passive triaxial (ADP) can then be computed.
Figure 3.3.1 : Undrained Shear Strength Depends Upon Shear Surface Inclination.
For a general value of the shear surface inclination BETA the following interpolation formula is used : Su(BETA) = SuD + (SuA - SuD)*sin(2BETA) , BETA > 0.0 (3.3.1) Su(BETA) = SuD - (SuP - SuD)*sin(2BETA) , BETA < 0.0 (3.3.2)
The basic Su0 values can be given by 3 different methods : 1. Given as a constant value for each material.
2. Given as a broken line with depth at vertical X sections.
3. Given as values at the nodal points of the mesh.
For each point (X,Z) the resulting Su0 value is taken as the sum of these three values. When values
at nodes are to be included, a weighted average of the element nodal point values is used as shown
on Figure 3.3.2 below.
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Figure 3.3.2 : Mesh Numbering and Procedure for Weighted Average of Values Specified at Nodal Points.
The weighted average at point (X,Z) is found as :
DIV = 1/D1
2+ 1/D2
2+ 1/D3
2+ 1/D4
2(3.3.3)
Su0(X,Z) = (Su0(11)/D1
2+ Su0(15)/D2
2+ Su0(14)/D3
2+ Su0(10)/D4
2) / DIV (3.3.4) where D is the distance from the point (X,Z) to the nodal point considered.
Cohesion
The cohesion value c given for each material is used in the Mohr-Coulomb expression for the failure shear stress τ :
τ = c + σ’ ⋅ tan(ϕ’) (3.3.5)
where σ’ is the effective normal stress on the shear surface and ϕ’ is the effective angle of internal friction.
The c value is assumed to be isotropic, i.e. independent of shear plane inclination.
One may want to analyse cases with both sand and clay layers on an effective stress basis, but to maintain the anisotropic ADP type undrained shear strengths explained above for clay layers. In order to allow this, BEAST will check if cohesion and friction are both zero. In that case, the cohesion is replaced by the Su(BETA) value found above, and the friction angle maintained as
zero.
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Angles of Internal Friction
An angle of internal friction, PHIANG, is read for each material. In addition, the user may specify two values, PHIREF and PHIRED, to model a friction angle that depends upon the effective normal stress SIG :
PHI(SIG) = PHIANG - PHIRED*Log10(SIG/PHIREF) (3.3.6) The PHI angle is directly used by BEAST in the plane strain type calculations carried out. Any pos- sible modification of a laboratory triaxial angle of internal friction to account for plane strain effects is the responsibility of the user.
Parameters for Undrained Effective Stress Analysis (UESA)
BEAST may carry out an undrained effective stress analysis, i.e. the excess pore water pressures are to be calculated as a part of the solution. Appendix B gives the theoretical basis for this analysis.
In order to allow such calculations, the following soil parameters are needed for each material :
* B-FACTOR : DEL.U = B * (DEL.SIGAVR - D * DEL.SIGDEV) (3.3.7) * K-NOT : Initial effective stress ratio SIG30/SIG10
* B-SIG2 : Intermediate principal stress ratio , SIG2 = SIG3 + B * (SIG1 - SIG3) (3.3.8) * D-FACTOR : Shear contribution to DEL.U, equation (3.3.7) above.
For real soils the D-factor will in general not be a material constant, but depend upon stress level and direction of stress changes. BEAST therefore allows specified Su0 values, multiplied with SuADP ratios, to be interpreted as D-factors.
Rigid Materials
The soils in a slope or near a foundation may contain strong structural elements like a wall or a con- crete base. The presence of such obstructions may be modelled by the rigid material option. If a material is given a negative strength, for example Su = -50 kPa or φ' = -25°, shear surfaces that cut through such a material gets a safety factor of 99.999 and a score of 7.777. Such surfaces thus become non-critical. The interslice strength is found using the absolute value of the soil strength parameters, and the negative value has no effect.
Soil Properties Used by BEAST
The above explained how soil properties are obtained at a single given point (X,Z). For each slice we need average values along the faces 1, 2 and 3, see Figure 3.2.1.
At face 3, the shear surface, the strength values (tan ϕ’, c and Su) are found as the average of the values determined in 5 points along the slice bottom.
At face 2 (which is face 1 for next slice), the value is found as :
V avr = (V2 + 2*V23 + V3) / 4.0 (3.3.9)
where V2 and V3 are values at top and bottom of face 2, and V23 is the value at mid height. It should
be noted that this averaging procedure may influence the computed results in the case of several
layers with very different properties.
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3.4 Pore Water Pressures and Forces
BEAST has a number of different options that can be used to generate PWP values at any point within or at the surface of the soil body considered. Figure 3.4.1 illustrates the different options, and they are explained in some detail below.
Hydrostatic Pore Water Pressures
In order to simplify program input and to save computer time, the user specifies if the PWP is hydrostatic or not. If hydrostatic conditions are specified, the PWP is computed as :
PWP = (Z - WT) * GAMWAT (3.4.1)
where Z is the Z co-ordinate of the point, WT is the Z co-ordinate of the water table and GAMWAT is the unit weight of water.
The PWP input data includes the minimum allowed PWP value (could be negative as a result of capillary tension, referred to as matrix suction below). If the PWP value found by equation (3.4.1) or by the below non hydrostatic procedures, is lower than this minimum, the minimum is used. For non- hydrostatic pore pressures the minimum PWP value may be multiplied by a material dependent factor, see Option E below.
Non-Hydrostatic Pore Water Pressures
In case the user has specified non-hydrostatic PWP, BEAST will run through all possible options and add the individual contributions found, with the exceptions explained at the end of this section.
Option A : Given PWP With Depth at Vertical Sections
This option may in principle be used to specify any variation of PWP. The user gives the position of a number of vertical profiles (X-lines). The PWP variation with depth at each profile is given point by point. For any point (X,Z) BEAST will then determine the PWP value by linear interpolation or extra- polation.
When the given point (X,Z) is located between two profiles, as shown on Figure 3.4.1, interpolation is carried out along a line parallel to the line that connects the two top points in each profile.
For points located before the first X-line, or after the last X-line, interpolation is done along a horizontal line.
Points above or below the first or the last point on the X-line are given PWP values equal to the first or the last value.
Option B : PWP as a Ratio of Total Overburden
This way of giving PWP is often used in connection with dams and embankments. For a given point (X,Z) BEAST first determines the material identification number, Section 3.3, and the corresponding value of Ru. The PWP value is then computed as :
PWP = Ru * (Z - ZSURF) * GAM (3.4.2)
where ZSURF is soil surface Z-level at X and GAM is the average unit weight, taken at mid height.
It should be noted that BEAST will interpret a negative Ru value to mean that PWP shall still be
computed from equation (3.4.2), with changed sign. However, none of the other options A,C,D,E or F
shall be included. Such a procedure may be needed for example in the case of a dam with a clay
core.
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Figure 3.4.1 : Different Options That May be Used to Specify Pore Water Pressures
Option C : Given PWP Unit Weight
This option assumes a linear variation with depth with zero PWP at the Z-level of the given water table.
If the soil surface above the point (X,Z) is not submerged, the PWP value is computed as :
PWP = (Z - WT) * GAMPWP (3.4.3)
where WT is the water table level and GAMPWP is the pore water given unit weight.
If the soil surface point is submerged, i.e. ZSURF is greater than WT, the PWP is computed as : PWP = (ZSURF - WT) * GAMWAT + (Z - ZSURF) * GAMPWP (3.4.4) where ZSURF is the soil surface Z level above the point and GAMWAT is the given unit weight of water.
This option C will not be used if option A is specified, as option C could give a problem for cases with
water on one side only. BEAST assumes that the specified water table extends over the entire sys-
tem at the same Z level. If this assumption shall not be made, PWPs must be specified by option A,
and BEAST will calculate the corresponding ground water levels, and use these values for load
calculations.
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Option D : PWP Values Given at Mesh Nodal Points
This option will in principle allow any variation of the PWP, provided a sufficiently fine mesh is gene- rated. The nodal point PWP values are read from input file NF15. Procedures used to compute a weighted average value at point (X,Z) are identical to those described for undrained shear strength in Section 3.3 above.
Option E : PWP Values Specified for Soil Material
Each material has been given a PWP value that is associated with that material only. Under most conditions the value would be zero. However, the option may be used to describe a certain layer or an area that is charged with PWP values different from those in the surrounding soil volume.
The user may want to specify different minimum allowed PWP values for the different materials, for example in a slope stability analysis where matrix suction shall be included in silts but not in sands.
Analyses of this type are described by Öberg (1997) and SGI (1998). The D-parameter read as input may be used for this purpose as described in Section 4.2.
Option F : PWP Values Specified for General Shear Surfaces
If the user has specified non-hydrostatic PWP values, and if general shear surface(s) shall be read as input, BEAST expects to find PWP values for each surface together with the co-ordinate values.
This option allows an easy input of PWP values along a pre-determined shear surface. The specified values will be added to the PWP values computed from any of the above options.
Option G : UESA, Undrained Effective Stress Analysis
BEAST allows an undrained effective stress analysis to be carried out, see Svanø (1981) and Svanø
& Nordal (1988) for a description of the principles of the method.
In this case the PWP values are not explicitly given, but they are calculated from stress changes along the shear surface. Stress changes and PWP changes are assumed linked by the following equation, Janbu (1979) :
DEL.U = B * (DEL.SIGavr - D * DEL.SIGdev) (3.4.5) The B- and D-parameters are given for each material. BEAST allows the D-parameter to depend upon inclination of the shear plane. Details of assumptions involved and solution procedure are given in Appendix B.
Combination of Different PWP Options
The above will allow any variation of PWP to be modelled by the user. If non-hydrostatic PWP was specified, the main rule is that each PWP contribution is calculated and added to the others to form the resulting PWP. However, the following exceptions from this rule exist :
1. A negative Ru value for a material is used to flag that Ru contributions only are to be included for that material.
2. If PWP values at vertical X lines were specified, PWP values calculated by option C (given PWP and water unit weights) are not included. This allows different water levels at two sides of an embankment to be modelled.
3. In case of UESA, all other PWP contributions are set to zero, for all materials.
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Pore Water Pressure Forces
The above can be used to find the resulting PWP at any point (X,Z). What is needed below is the resulting PWP force acting against the three slice faces 1, 2 and 3 shown on Figure 3.2.1.
In the case of hydrostatic PWP, the corresponding forces against the faces, and the points where they act, can be computed exactly.
In the case of non-hydrostatic PWP, an approximate numerical integration must be carried out.
BEAST computes the PWP values in 5 points along face 3 at the slice bottom (shear surface), and in 10 points along face 2 (interslice vertical contact surface).
3.5 Load Calculation
Each slice may be subjected to the following types of forces, that will be independent of the safety factor :
* Vertical and horizontal self weight forces.
* Forces due to given external line loads and distributed stresses.
* Water pressures against the top of the slice and in cracks.
* PWP forces against slice faces 1, 2 and 3.
* Side shear forces in case a non plane strain situation shall be simulated, calculated initially with safety factor = 1.0.
* Axial and lateral soil nail forces, calculated initially with safety factor = 1.0.
Self Weight Forces
The area of each slice is computed assuming a straight soil surface between the two top points 1 and 2, Figure 3.2.1. If a broken soil surface line exists over the slice width, an approximate correction is carried out.
If more than one material is specified, an accurate average unit weight is calculated for each slice in the case of horizontal layering.
If material triangles are used, or zero horizontal layers were specified, the average unit weight is determined by a numerical summation with 10 X increments and 30 Z increments for each slice.
The vertical force acting through the slice centre 5 is then found as :
WZ = AREA * GAMAVR * ACCZRT (3.5.2)
where AREA is slice area and ACCZRT is an acceleration ratio, equal to 1.0 if normal gravity acts. In the same manner, the horizontal force through point 5 is computed as :
WX = AREA * GAMAVR * ACCXRT (3.5.3)
where ACCXRT is the acceleration ratio in the X-direction, equal to 0.0 unless earthquake type
loading shall be included.
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Given External Line Loads and Stresses
External line loads may act vertically and horizontally, and at any point within or above or below the soil volume considered. For each slice line loads located at a vertical line within the slice are included, even if the line load is acting above the soil surface. However, line loads located under- neath the shear surface are not included.
Distributed stresses are assumed to act at the soil surface. For each slice an exact computation of forces and moments is carried out, even if discontinuities exist over the slice.
Water Pressures on Top of Slice and in Cracks
An exact calculation of water pressure forces and moments is carried out for each slice based upon slice points 1 and 2 co-ordinates, water table and water unit weight. If vertical sections with PWP values were specified, the water table elevation above each slice (may vary along the profile) is calculated from these values.
At the first slice a crack may exist on the left side. The depth of such a crack, and the depth of water in the crack, is part of the input data. The procedure used by BEAST to handle such cracks is shown on Figure 3.5.1. The starting point of the shear surface is moved from point 4 to point 4'.
Figure 3.5.1 : Procedure Used to Include Cracks and Water in Cracks.
PWP Forces
Methods used to compute these forces were described in Section 3.4. They enter the computations just like the other forces described above, and are summed together with them at slice centre point 5.
This results in two known forces WX and WZ, acting through point 5, and one moment WM.
In the case of UESA, the PWP forces are found by an iterative procedure as described in Appendix B.
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Side Shear Forces
In case the system analysed has limited length normal to the paper plane (Y-direction), the user may want to include a correction to account for the shear forces that may act upon the two side (end) surfaces. Assuming a safety factor of 1.0, BEAST finds the side shear force at each slice by the following procedure :
1. Compute the average effective unit weight of the slice from the total unit weight at the slice centre point 5 and the water table level.
2. Compute average horizontal stress SIGH in the Y- direction assuming Ko' = 0.5.
3. Compute force FY as SIGH * AREA 4. Compute side shear force SS as :
SS = (C2*AREA + FY*tan(PHI2)) * SIDSHR (3.5.4)
where C2 is cohesion or undrained strength at slice face 2, PHI2 is the friction angle at face 2 and SIDSHR is a factor given as input.
All forces in BEAST are computed assuming a unit length in the Y-direction. If, as an example, the system analysed has a length of 25 m in the Y-direction, and we want to include full side shear at both end surfaces, the value of SIDSHR should be given as :
SIDSHR = 2.0 / 25.0 = 0.08 (3.5.5)
This option should be used with care in connection with shallow footings on sand subjected to mainly vertical loading, as a positive SIDSHR will always increase the safety factor, whereas reality may be the opposite.
The side shear force SS is assumed to act through the mid-point between the shear surface and point no. 5. Its direction is assumed parallel to the shear surface, and it is always acting against the displacements. When the system of slices is being solved, the above shear force SS is divided by the safety factor.
Soil Nail Forces
Forces from piles and/or soil nails were included in revision 3 of the BEAST program. The
procedures used to calculate the axial and the lateral soil nail forces are described in some detail in Appendix D. These values are first calculated assuming a safety factor of 1.0 on soil skin friction and on the structural strength. During the iterative solution of the system of slices, the pile/nail forces are divided by the same assumed safety factor as the one used on the soil strengths, and included in the equilibrium equations.
3.6 Governing Equations
Figure 3.6.1 shows a typical slice with the forces acting upon it, and the locations of these forces.
The pore water pressure forces U1, U2 and U3 (and their locations) are calculated in advance from
the pore water pressures found as described in Section 3.4. These forces are then included in WX,
WZ and WM acting at the slice centre point 5.
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Figure 3.6.1 : Single Slice With Forces and Moment Arms.
The values shown are :
E1, E2, P Effective normal forces.
T1, T2, S Shear forces.
WX, WZ, WM Known forces and moments referred to the slice centre.
Includes self weight, given external loading and pore water pressures.
SS Side shear force.
H1, H2, H3 Location of normal forces.
HS Location of side shear force.
BETA Shear surface inclination.
All values are positive when acting as shown on Figure 3.6.1.
The forces shown on Figure 3.6.1, and also the equations (3.6.1) to (3.6.14) shown below, do not for
reasons of simplicity include the forces from piles/soil nails. Appendix D explains how such forces
are taken into account and presents the corrected equations that are actually used in the calculations.
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Program BEAST solves a system of slices from the left to the right (increasing X-value) with an assumed or a known factor of safety. At the first slice, E1 and T1 will always be zero, any known forces acting here would be included in WX, WZ and WM.
After a slice has been solved, we know all the above values. This means that E1, T1 and H1 for the next slice are also known, as they must equal E2, T2 and H2 for the present slice. We can therefore write the following table of known/unknown geometry and forces for a single slice :
Table 3.6.1 : Single slice known and unknown values
Known Unknown
Geometry : H1,HS H2, H3
Forces : E1, T1, SS E2,T2
WX, WZ, WM P, S
For each slice we can write 3 equations related to equilibrium and 1 equation for failure shear stress at the shear surface :
Sum X-forces = 0.0
E1 + WX - E2 + P * sin(BETA) - (S+SS) * cos(BETA) = 0 (3.6.1) Sum Z-forces = 0.0
T1 + WZ - T2 - P * cos(BETA) - (S+SS) * sin(BETA) = 0 (3.6.2) Sum moments w.r.t. point 3 = 0.0
B = X2-X1, H4 = Z3-Z4, B5 = X3-X5, H5 = Z3-Z5
T1 * B - E1 * (H1+H4) + WM + WZ * B5 - WX * H5 + SS * HS + E2 * H2 - P * H3 = 0 (3.6.3) Fully mobilised shear strength at face 3
S = (C3 * L34 + P * tan(PHI3)) / SF (3.6.4)
where SF is the assumed or known safety factor, C3 the cohesion at face 3, PHI3 the friction angle at face 3 and L34 the shear surface length.
For the unknown shear force T2 we can write an equation similar to (3.6.4) :
T2 = R * (C2 * L23 + E2 * tan(PHI2)) / SF (3.6.5)
where R is an unknown roughness value between -1.0 and +1.0.
If the two shear force equations are introduced into the three equilibrium equations, we obtain after
some simple arithmetic :
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Sum X : P*C11 - E2 = C12 (3.6.6)
Sum Z : P*C21 + R*E2*tan(PHI2)/SF + R*C22 = C23 (3.6.7)
Sum M : P*H3 - E2*H2 = C31 (3.6.8)
The C-coefficients are given by :
C11 = sin(BETA) - tan(PHI3)*cos(BETA)/SF (3.6.9)
C12 = -E1-WX+SS*cos(BETA)/SF+C3*L34*cos(BETA)/SF (3.6.10)
C21 = cos(BETA) + tan(PHI3)*sin(BETA)/SF (3.6.11)
C22 = C2*L23/SF (3.6.12)
C23 = T1+WZ-SS*sin(BETA)/SF-C3*L34*sin(BETA)/SF (3.6.13)
C31 = T1*B - E1*(H1+H4) + WM + WZ*B5 - WX*H5 + SS*HS/SF (3.6.14) The 3 equations (3.6.6 to 3.6.8) are the governing equations for any system of slices. The only assumptions made so far are :
1. The Mohr-Coulomb failure criterion applies, equations (3.6.4) and (3.6.5).
2. The factor of safety is constant through the system of slices.
It is seen that the 3 equations contain the following unknowns : P, E2, R, H2 and H3, i.e. 5 values. In order to solve this system one must therefore make 2 assumptions. It must be expected that it will be easier to guess geometry constants H2 and H3, and interslice roughness R, rather than actual forces P and E2. Three main possibilities therefore seem to exist :
A. Assume H2 and H3, compute R and forces.
B. Assume H3 and R, compute H2 and forces.
C. Assume H2 and R, compute H3 and forces.
The well known procedures by Morgenstern and Price (1965), and Spencer (1967), are of type B.
The generalised procedure of slices first published by Janbu (1957,1973) is in principle of type C.
However, the interslice shear force T, rather than the roughness R, is "assumed" by Janbu, i.e.
calculated from moment equilibrium of the vertical interface between two slices.
Other procedures, like Fellenius (1927) and Bishop (1955) may fall outside this system, as these procedures do not satisfy all the equilibrium requirements. The reader may want to consult Wright (1969) for a detailed description of such procedures and the associated assumptions.
BEAST Revision 2
After several years of experience with the BEAST program it was seen that the selected type B
solution procedure now and then gave problems related to non-convergence and solution score (see
Section 3.9). It was therefore decided to adapt a somewhat modified solution technique as described
in Section E4 of Appendix E.
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3.7 Solution Procedures, Stability and Bearing Capacity
Revision 4 of program BEAST may use five different solution methods. The governing equations and procedures used for each of these methods are described in Appendix E.
These methods all involve a potential numerical problem. In order to determine the P-force against the slice bottom, a division must be carried out, and the divisor could be zero or negative, depending upon shear surface geometry and soil properties. This potential problem is discussed below, followed by comments related to (1) the BEAST simplified total stress solution for circles, (2) the Swedish combined analysis method, and (3) a summary of the BEAST revision 4 extensions.
Potential Numerical Problem
With an assumed value of the safety factor SF, we can calculate the coefficients C11 to C31 from equations (3.6.9) to (3.6.14). Combining equations (3.6.6) and (3.6.7) gives :
DIV = C21 + R*tan(PHI2)*C11/SF (3.7.1)
P*DIV = C23 + R*(tan(PHI2)*C12/SF - C22) (3.7.2)
Having found the P force, the two remaining unknowns are calculated from :
E2 = P*C11 - C12 (3.7.3)
H2 = (P*H3 - C31) / E2 (3.7.4)
For slope stability and bearing capacity problems the force E2 shall be zero at the last slice. After the first pass through the system with an assumed SF, it will therefore be necessary to repeat the
process with other SF assumptions until the E2 force becomes smaller than a user defined con- vergence criterion.
In the case of total stress analysis it is found that the E2 force at the last slice can be expressed as :
E2 = E2LIM - AA / SF (3.7.5)
E2LIM = SUM(WX + WZ*tan(BETA)) (3.7.6)
In the case of effective stress analysis there is a more complex relationship between E2 at the last slice and SF. During the iterative solution process care must therefore be taken to obtain the first solution E2 = 0.0 as SF is decremented. Figure 3.7.1 shows an example of calculated relationship between SF and E2. It is seen that discontinuities exist when SF is lower than say 0.85 for the example shown on the figure.
What happens is a zero division when calculating P from equation (3.7.2). We have that :
DIV = C21 + R*tan(PHI2)*C11/SF (3.7.6a)
Taking C11 and C21 from (3.6.9) and (3.6.11) we obtain :
DIV = 1 + tan(PHI3)*tan(BETA)/SF + R*tan(PHI2)*(tan(BETA) - tan(PHI3)/SF)/SF (3.7.7)
For the example shown on Figure 3.7.1 we have :
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BETA = 45 - PHI/2 = 27.5 degrees (3.7.8)
tan(PHI2)/SF = tan(PHI3)/SF = tan35/0.85 = 0.82 (3.7.9)
DIV = 0.57 - R * 1.10 (3.7.10)
DIV thus becomes zero and then negative when R is 0.52 or higher.
The above demonstrates that in any limit equilibrium procedure it will be necessary to ensure that the shear surface inclination in the passive zone is compatible with the friction angles PHI2 and PHI3, and the interslice roughness factor R. In revision 4 of BEAST an option was therefore included that allows an automatic reduction of a too steep shear surface exit angle.
Using the above expressions, the initial distribution of the P-forces is established. BEAST may then modify this solution by the procedures explained in Section E4 of Appendix E, and calculate all unknown forces, moment arms and interslice roughness values.
We then have a complete solution, and we can inspect the solution in order to determine its quality.
Such an inspection is done automatically by BEAST and the result expressed as a single number referred to as "score". Score equal to zero means that the solution meets all quality requirements.
The higher the score value, the poorer the solution. The method used by BEAST to calculate the score value is explained in detail in Section 3.9 below.
The score concept allows BEAST to try different assumptions for the interslice roughness factor R, calculate the SF and the score value, and to select as final solution the R assumption that gives the lowest score value. The R assumptions tried by BEAST are the initial Ro values specified by the user multiplied by factors that will cover the range R = 0.0 to 1.0.
In case several R assumptions all lead to zero score, BEAST takes the solution with the highest safety factor as the wanted solution.
From the above it follows that the moment equilibrium equation for each individual slice (3.6.8) is only used indirectly, i.e. to find the position H2 of the line of thrust which will influence the calculated score value. For the last slice the moment equation is used to calculate H3 rather than H2.
Simplified Solution, Circles and Total Stresses
For cases that involve both circular shear surfaces, and total stress analysis, BEAST will use a simplified solution method that only considers moment equilibrium.
The area of the slices, and the shear surface lengths, are increased to include the small circle
segment underneath the shear surface. Undrained strengths at the shear surface, slice centre forces etc. are calculated by the standard BEAST procedures as explained in this report.
After the safety factor is found, all slice forces except S are set to zero. The score value for these solutions is set to 9.999.
Swedish Combined Analysis, BEAST Revision 3
Analysis of slope stability and bearing capacity has traditionally been carried out as either effective
stress analysis, or as a total stress analysis. It may be argued that a slope stability analysis should
be carried out as a combination of the two methods, where the lowest strength obtained by the two
analyses at any point is used, see for example Sällfors & Larsson (1984).
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BEAST allows this type of analysis to be carried out. For the given shear surface an effective stress force equilibrium solution is established with the given roughness values. With known P and E2 normal forces the corresponding shear strengths can be calculated from equations (3.6.4) and (3.6.5). These shear strengths are then compared to the given undrained strength values. If the undrained strength values are lower, the cohesion at that face is replaced by the undrained strength, and the friction set to zero.
A normal BEAST effective stress analysis is then carried out using the modified strength values.
BEAST Revision 4
This revision was made primarily because of small errors that now and then occurred for the
combined analysis. The combined analysis method compares the effective stress based and the total stress based shear strengths at the slice bottom, and uses the smaller value. A combined analysis solution should therefore always give a safety factor that is equal to, or lower than, the safety factors from the effective stress and the total stress solutions. Unfortunately, this was not always the case for BEAST revision 3.
It was therefore decided to completely re-write the BEAST combined analysis procedures. This provided an opportunity to also expand and improve the solution methods that could be used by BEAST. These revised procedures are described in the new Appendix E.
At the same time it was decided to also include :
* A rigid material option that may be used to model the presence of e.g. a foundation base. Shear surfaces that intersect a zone with a rigid material are given a safety factor of 99.999 and a solution score (see below) of 7.777.
* An option that allows BEAST to automatically reduce the shear surface
exit angle through frictional materials. This option is explained in Section 4.2
of the report.
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Figure 3.7.1 : Example Relationship Between Assumed Safety Factor SF and
Horizontal Force E2 at the Last Slice.
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3.8 Solution Procedures, Earth Pressures
Earth pressure calculations can be handled by procedures very similar to those used for slope stability and bearing capacity calculations, as pointed out by Nilmar Janbu already some 45 years ago, Janbu (1957).
Figure 3.8.1 : Earth Pressure Calculations
As part of the input data read by BEAST, the user specifies if bearing capacity or earth pressure calculations shall be carried out. BEAST also reads the location of the wall, XW, the height of the wall, HW, and the wall roughness (relative magnitude and sign of the shear force T2).
Earth pressure calculations are carried out with the same basic assumptions as described for stability and bearing capacity cases in Section 3.7. This means that the position H3 of the normal force P on the bottom of the slice is known, together with the interslice roughness R. BEAST assumes a linear variation of R from R1 at the start of the shear surface to RW at the wall itself. R1 and RW are user supplied values.
For a given shear surface BEAST then only needs a safety factor (to be specified by the user) in order to compute through the system of slices, and end up with the corresponding earth pressure values E2, T2 and H2 as shown on Figure 3.8.1.
If a positive safety factor is specified, the E2 force computed will be the active earth pressure, which
is the situation shown on Figure 3.8.1. If a negative safety factor is specified, all shear forces S, SS
and T will act in the opposite direction, and the E2 force computed will be the passive earth pressure.
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3.9 Solution Quality Control
Once a solution has been obtained, BEAST carries out a fairly detailed check for two reasons : 1. To identify obvious errors or problems and present an error message to the user.
2. To find a measure for the quality of the solution, i.e. how close it is to what one would consider as a "perfect" solution.
Error Messages
The checks carried out by BEAST include :
* Check that P and S forces at each slice bottom really gives a degree of strength mobilisation equal to the computed safety factor.
* Check that the three equilibrium requirements are satisfied for each slice.
* Check that computed forces E2 and T2 at last slice are zero for stability and bearing capacity cases.
The above checks should not really be necessary, as the requirements are part of the equations solved. However, programming errors or other unintended conditions could lead to results that do not meet the above requirements.
Solution Quality, Score
The above checks are aimed at solution errors and results that are obviously wrong. Even if a solution passes these checks, the solution quality may still be rather poor. We therefore need a system by which it is possible to find a single number that reflects how near the present solution is to what we would consider a "perfect" solution.
For this purpose BEAST operates with a value called "score". Score = 0.0 is considered to be a perfect solution that has the following qualities :
1. All normal forces P and E2 are positive. Negative values may be specified as allowed.
2 The interslice degree of shear mobilisation R is between +1.00 and -1.00.
3. The normal force P acts within the middle third of face 3.
4. The normal force E2 acts within the middle third of face 2.
The punishment ERR given in case some of these requirements are not met is indicated on Figure 3.9.1.
The numerical value of "score" is then calculated as :
SCORE = SUM (ERR) / N (3.9.1)
where the sum is taken over the N slices.
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Solution Score for Some Special Cases
Some of the solution methods used by BEAST (see Appendix E) are incomplete, i.e. some of the slice forces and/or moment arms shown on Figure 3.6.1 are not known. For such cases the score value is set to one of the values listed below.
6.666 Force equilibrium solution, moments are neglected 7.777 Shear surface intersects a rigid material, no analysis 8.888 Bishop's simplified method, horizontal forces not known
9.999 Circular shear surface in clays, moment equilibrium only, only S-forces known
Figure 3.9.1 : Procedures Used to Find Solution Score
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4.0 USER'S GUIDE
4.1 General System Description
Program BEAST operates interactively, i.e. questions, different options and messages are displayed at the user's screen, and the user must give the instructions needed from his keyboard. In order to limit the user/machine communication, a formatted input file, NF14, that contains most of the data needed is read by BEAST at the start of the run.
File NF14 may contain comment lines for detailed explanation of the parameters used. BEAST generates a new input file NF15 with such lines removed. Section 4.2 presents a detailed description of file content.
The figure below shows the different parts of the system. The file names indicated are the names that BEAST either expects to find in the present directory, or the names that BEAST will give to the result files.
The files NF5 and NF6 may be replaced by the files INP and RES, see IPRTTP in Section 4.2
Figure 4.1.1 : BEAST General System.
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4.2 Input Data File NF14
The next pages show an example input file to BEAST for the below combined slope stability and bearing capacity problem.
Figure 4.2.1 : Input File NF14 Demonstration Example
The remaining pages of this section present the NF14 input file for the above example, followed by a detailed explanation of the different values BEAST may read from input file NF15, which is identical to file NF14 except for the comment lines, see below.
Notice that the line numbers included in the example input file are there for reference purpose only.
They should not be part of an actual BEAST input file.
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1---- BEAST PROGRAM DOCUMENTATION REPORT SECTION 4.2 TEST EXAMPLE 2---- SLOPE WITH SURFACE LOADING 11 Apr 2003 3---- * 4---- * Date Sign Log of file modifications 5---- * --- ---- --- 6---- * 13 Oct 1993 cjfc Original version, units used are : kN & m 7---- * 11 Apr 2003 cjfc Include extra input line with MISC1-5 and VAL1-5 8---- * 9---- 10---- ****************** CONTROL SECTION 11---- 1.0 1.0 CONFRC,CONLTH CONVERTION FACTORS ON FORCES AND LENGTHS 12---- 1.0 1.0 FCTSUC,FCTTAN MATERIAL FACTORS ON SU,C AND TAN(PHI) 13---- 1 IDTYP SOLUTION TYPE (1=STAB/BEARING 2=EARTH PRESS) 14---- 01 IDEFTO ANALYSIS METHOD & TYPE, E.G. 31 = BEAST-2003 & EFF.STRESS 15---- 1 NUMGEN NUMBER OF GENERAL SHEAR SURFACES 16---- 0 NUMSLC NUMBER OF SLICES (ZERO OK FOR GENERAL SURFACES) 17---- 0.0 SIDSHR SIDE SHEAR FACTOR (0.0=PLANE STRAIN , 2.0/LENGTH=MAX) 18---- 0.00 0.00 VALUES FOR H3-ASSMPTN (H3(X)=H31+(H32-H31)/XTOT*X) 19---- 0.00 1.00 0.00 VALUES FOR R-ASSMPTN (R(X)=R1+(R2-R1)/XTOT*X+H(X)/HMAX*R3) 20---- 0 ITENSP ALLOW P-FORCE TENSION IN SCORE CALCULATION (0=NO 1=YES) 21---- 1 ITENSE ALLOW E-FORCE TENSION IN SCORE CALCULATION (0=NO 1=YES) 22---- 0 JPRINT TRACE PRINT CODE (0=NON 1=LIM 2=TRACE 3=DETLD TRACE) 23---- -1 IPRTTP FILE NF16 PRINT TYPE FOR SLICE OUTPUT (1=FORCES 2=STRESSES) 24---- 2 JPLOT CODE FOR PLOT(S) ON NF16 (0=NO 1=YES 2=+PWP/SU0 3=+MESH) 25---- 0.000 CRTFRC CONVERGENCE CRITERION , FORCES (DEFAULT=SUM(FZ)/1.0E4) 26---- 2.000 CRTSCR CONVERGENCE CRITERION , SOLUTION SCORE 27---- C = 0.000 : FIND ZERO SCORE SOLUTION WITH HIGHEST SF 28---- C = 0.001 TO 0.999 : TAKE FIRST SOLUTION WITH LOWER SCORE 29---- C = 1.000+ : USE INTERSLICE ROUGHNESS FACTOR 1.0 30---- C MISC1 MISC2 MISC3 MISC4 MISC5 VAL1 VAL2 VAL3 VAL4 VAL5 31---- 0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 32---- C MISC1=1 flags that BEAST is allowed to change the shear surface exit angle 33---- 34---- ****************** GEOMETRY SECTION 35---- 6 NUMXLN NUMBER OF X-LINES WITH SURFACE, ROCK AND ELEMENT SPECS 36---- 4 NUMELZ NUMBER OF ELEMENTS IN Z-DIRECTION 37---- 2 NUMLAY NUMBER OF HORIZONTAL LAYERS 38---- 1 NUMTRI NUMBER OF MATERIAL I.D. TRIANGLES 39---- X-VALUE Z-SURFACE Z-ROCK NUMBER OF X-ELEMENTS TO NEXT X-LINE 40---- 0 20 44 1 41---- 10 20 44 7 42---- 80 20 70 4 43---- 120 47 85 2 44---- 140 60 85 4 45---- 180 60 85 0 46---- 00 00 00 0.0 0.0 NP1,NP2,NSTEP,ZN1,ZN2 NODE NEW Z , NP2=MAX TERMINATES 47---- 00 00 00 0 NE1,NE2,NSTEP,MAT ELEMENT MATRL , NE2=MAX TERMINATES 48---- LAYER Z-BOTTOM MATERIAL-I.D.
49---- 1 40 1 50---- 2 100 2 51---- TRIANGLE MATERIAL X1 Z1 X2 Z2 X3 Z3 52---- 1 3 0 121 150 55 1.0E6 55 53---- 0 0 0 XWALL,HWALL,RWALL WALL SPECIFICATIONS (LOCATION,HEIGHT,ROUGHNESS) 54---- 55---- ****************** MATERIAL PROPERTIES SECTION 56---- 3 NUMMAT NUMBER OF DIFFERENT MATERIALS 57---- 0 NUMXSU NUMBER OF VERTICAL X-LINES WITH GIVEN SU-VALUES 58---- 0 NODSU NUMBER OF MESH NODAL POINTS WITH GIVEN SU-VALUES 59---- 5.0 CRACKZ SURFACE OPEN CRACK DEPTH 60---- 2.0 CRACKW WATER DEPTH IN OPEN SURFACE CRACK 61---- 0.0 PHIREF FRICTION ANGLE REFERENCE PRESSURE 62---- EFFECTIVE STRESS ANALYSIS STRENGTH PARAMETERS (ALWAYS INCLUDE , ZERO OK) 63---- MAT GAMTOT COHSN PHIANG PHIRED PWPMAT RU-MAT B-FACT K-NOT B-SIG2 D-FCT 64---- 1 18 20 35 0 0 0 0 0 0 0 65---- 2 21 10 25 0 0 0 0 0 0 0 66---- 3 21 0 40 0 0 0 0 0 0 0 67---- TOTAL STRESS ANALYSIS STRENGTH PARAMETERS (ALWAYS INCLUDE , ZERO OK) 68---- MAT GAMTOT SUA/SU0 SUD/SU0 SUP/SU0 SU0-MAT (A:ACTIVE D:DIRECT P:PASSIVE) 69---- 1 18 1.00 1.00 1.00 0 70---- 2 21 1.00 1.00 1.00 0 71---- 3 21 1.00 1.00 1.00 0 72---- X-LINE X-COORD Z-POINTS LINE 1 : Z-VALUES / LINE 2 : SU0-VALUES 73---- NODE SU0 (IF ALL NODES, SKIP NODE NUMBERS : SU0(1),SU0(2),...)
